Ideal Modulation Transfer Function Research Articles

Full 3-D modulation transfer function estimation of tomosynthesis system using modified Richardson-Lucy deconvolution.

Tomosynthesis systems are three-dimensional (3-D) medical imaging devices that operate over limited acquisition angles using low radiation dosages. To measure the spatial resolution performance of a tomosynthesis system, the modulation transfer function (MTF) is widely used as a quantitative evaluationmetric. We previously introduced a method to estimate the full 3-D MTF of a cone-beam computed tomography system using two-dimensional (2-D) Richardson-Lucy (RL) deconvolution with Tikhonov-Miller regularization. However, this method can not be applied directly to estimate the 3-D MTF of a tomosynthesis system, since the unique artifacts (i.e., shadow artifacts, spreading tails, directional blurring, and high-level noise) of the system produce several errors that lower the estimation performance. Varying positions of the negative pixels due to shadow artifacts and spreading tails cause inconsistent deconvolution performances at each of the directional projections, and the severe noise in the reconstructed images cause noise amplification during estimation. This work proposes several modifications to the previous method to resolve the inconsistent performance and noise amplification errors to increase the full 3-D MTF estimationaccuracy. Three modifications were introduced to the 2-D RL deconvolution to prevent estimation errors and improve MTF estimation performance: non-negativity relaxation function, cost function to terminate the iterative process of RL deconvolution, and regularization strength for noise control. To validate the effectiveness of the proposed modifications, we reconstructed sphere phantoms from simulation and experimental tomosynthesis studies in the iso-center and offset-center positions as well as estimated the full 3-D MTFs using the previous and proposed methods. We compared the 3-D render images, central plane images, and center profiles of the estimated 3-D MTFs and calculated the full widths at half and tenth maximum for quantitativeevaluation. The previous method cannot estimate the full 3-D MTF of a tomosynthesis system; its inaccurate negative pixel relaxation produces circular-shaped errors, and the mean squared error based simple cost function for termination causes inconsistent estimation at each directional projection to diminish the clear edges of the low-frequency drop and missing sample regions. Noise amplification from lack of noise regularization is also seen in the previous method results. Compared to the previous method, the proposed method shows superior estimation performance at reducing errors in both the simulation and experimental studies regardless of object position. The proposed method preserves the low-frequency drop, missing sample regions from the limited acquisition angles, and missing cone region from the offset-center position; the estimated MTFs also show FWHM and FWTM values close to those of the ideal MTFs than with the previousmethod. This work presents a method to estimate the full 3-D MTF of a tomosynthesis system. The proposed modifications prevent circular-shaped errors and noise amplification due to the geometry for limited acquisition angles and high noise levels. Compared to our previous method, the proposed scheme show better performance for estimating the 3-D MTF of the tomosynthesissystem.

Resolution degradation due to K-characteristic photon absorption in dual phosphor image receptors.

Image receptors based on the absorption of x rays by phosphor screens have a system resolution described predominantly by the modulation transfer function (MTF) of the phosphor screens utilized. This ideal MTF is modified by the presence of secondary effects within the imaging receptor such as scatter from the receptor cover, visible light crossover (in the case of screen film cassettes) and scatter generated within the phosphor itself, presumed to be almost entirely due to photoelectric interactions. In this paper the MTF characteristics resulting from the absorption of K-characteristic x rays emitted by one screen of a pair in an image receptor and absorbed by the adjacent screen (referred to as cross-fluorescence hereafter) are examined. This effect has been previously modeled [Med. Phys. 23, 1253 (1996)] and recently a computer program has been written to calculate intensity of the radial component of a point spread function (PSF) describing the above process. From this, the MTF of cross-fluorescence under varying conditions can be calculated. The model was applied to a dual screen experiment described in the literature [Med. Phys. 23, 871 (1996)], from which it was possible to show good agreement between calculated results and those derived from the measurement. The effect of screen thickness, screen separation, and phosphor material on the MTF of cross-fluorescence was investigated using simulated x-ray beam spectra in association with phosphor screen parameters. Results showed that the calculated MTF falls to below 0.1 at 1 cy/mm in all cases examined. This MTF was reduced further as the separation between the screens increased from that commonly used in a screen film cassette. Beam energy, phosphor thickness, and phosphor material had a minimal or no effect on MTF. The effect of cross-fluorescence on total image receptor MTF is to reduce the high-frequency components of that function by an amount that is in proportion to the scatter fraction of the effect.

High resolution X-ray imaging using a silicon strip detector

The authors present the first images and an initial evaluation of a scanned-slot X-ray imaging system based on edge-on silicon strip detectors and high-speed low-noise parallel processing ASICs. The authors have demonstrated noiseless single photon counting above a minimal threshold of 7.2 keV. Edge scans show negligible cross talk between different channels in the ASIC. The Modulation Transfer Function (MTF) has been measured and found to agree with the ideal MTF for 100 /spl mu/m pixel size. The first images are obtained at very low exposures and show the high performance of the system. The authors also present a way of enhancing the X-ray flux to a slot by using a refractive X-ray lens. They believe this focusing device will significantly enhance the potential for scanned-slot X-ray imaging.

Modulation transfer function for a large-area amorphous silicon image receptor

The modulation transfer function (MTF) of an amorphous silicon (aSi) sensor array was measured using proper sampling techniques to determine the edge spread function (ESF). The detector under study was a area detector (EG&G Heimann, RTM128) consisting of aSi photodiodes arranged in a square array. Two independent methods for calculating the presampling MTF were implemented, based on finely sampling the ESF measurements produced using 40 kV x-rays from a Faxitron microfocal spot x-ray tube. The two calculations of the detector's presampling MTF are in excellent agreement, and are within 20% at the Nyquist frequency when compared with the ideal MTF based only on the size of the detector elements. ESF measurements were also made at 6 MV on a Siemens MD-2 linear accelerator. A calculation of the system presampling MTF was performed which included effects from the linear accelerator source, the lead block used to create the high contrast edge, and the aSi detector response.

Optimal lateral interactions in a compound eye

1. This study considers a compound eye with a constant angular separation between the optical axes of individual ommatidia. When the modulation transfer function (MTF) of the system is a function which is constant for all spatial frequencies below the limit imposed by the sampling theorem, and zero otherwise, the eye will achieve the theoretically maximal information recording capacity. 2. Assuming a linear interaction between individual ommatidia, the presented computation (based on a Gaussian form of the angular sensitivity) leads to lateral interaction coefficients which provide the best approximation to the ideal MTF. Such lateral interaction greatly improves MTF's over those obtained when the ommatidia act independently. 3. Angular sensitivity functions which approach those obtained with the assumptions of optimal coupling between the ommatidia should be observable in second order cells of the lamina or medulla if the compound eye obeys this optimization. The improvement achieved by lateral interactions should be particularly significant for eyes which have a large overlap between the angular sensitivity functions of adjacent ommatidia.